I'm wondering if there is some proportion or scale one can use. As for example, if i want to reproduce the sound of a 6 ft piano i need sprakers with x inches woofer.

Of course i understand there are lot of variables involved. Even 2 pianos of same lenght may vary a lot.

But roughly speaking, is there any kind of criteria?

I'm not aware of a direct correlation. I think the rule of thumb is:

5" diameter is on the small side of acceptable, 6" drivers are probably better, since you need to reproduce some lower frequencies for the bass notes that are difficult for smaller drivers. This is regardless of whether you're trying to reproduce a 5' or 9' piano.

An 8" woofer seems to be the maximum sweet spot.

I had originally typed this reply without including "diameter," "woofer" and "driver" following the size, but then remembered that Pete14 is always lurking...

A relationship would be logical.

From the lowest note harmonics, only the third (and the following) harmonics are heard because the soundboard act as an high-pass filter. The bigger the soundboard the lower the heard partial are.

But I don’t know the relationship. When the piano is long enough, I suppose the width (constant : 88 keys) matters more than the length.

Don't look for relationships where no such is to be expected.

Or else risk falling into a trap. As in: The DOW index has often tracked closely with the price of butter in Bangladesh. Really. But we ought not read any meaning into that, right?

What matters is how much air the woofer can move and the enclosure it is in. Long excursion/throw woofers travel further laterally. A 5 inch long throw woofer might be equivalent to an 8 inch normal woofer. The design of the enclosure also is very critical. There are a number of designs, but the most common are acoustic suspension and bass reflex.

Bass horns, transmission line cases, resistive ports, and Helmholz resonators are examples of other bass enclosure designs, with resistive ports and Helmholz resonators being a variation on the basic bass reflex design. Bass horns are comparatively very efficient, and can fill a large space, but are themselves very large. Transmission line enclosures are very heavy. Most studio monitors use a bass reflex design, but some are acoustic suspension.

Pianos do not produce much deep bass because the soundboard of even a concert grand does not resonate below about 55Hz or so. The best way to choose audio monitors for base response is to look at the frequency response spec. Try to find a spec that has the measured frequency at which the bass response rolloff is stated as -3dB. You then can view those monitors as reasonable for producing content that goes that low.

Some classic examples of stereo speakers using the different enclosure designs.

1. Acoustic suspension - Acoustic Research, KLH, Advent, Electrovoice

eg The Advent

2. Bass reflex -- JBL, Cerwin-Vega

eg JBL L100

3. Helmholz Resonator -- Polk

eg Polk Monitor 10

4. Resistive Ports -- Dynaco, also called aperiodic design, basically a hybrid between bass reflex and acoustic suspension.

eg Dynaco A25

5. Bass Horn -- Klipsch

eg Klipschorn (corner horn)
or LaScala (folded horn)

6. Transmission Line -- never very popular due to high cost and very heavy enclosures, but bass is very accurate. PMC is a British studio monitor company that uses transmission line enclosures.

Some current tower speakers use a modified/simplified transmission line design and are more reasonably priced.

https://www.parts-express.com/dayto...mission-line-tower-speaker-pair--300-658

Does any of that serve to answer the original question?

I agree that the design of the enclosure is critical. Last year I added a pair of Presonus Eris E5 XT studio monitors (5-1/2" woofers) to my Privia PX-870, and now I most definitely do not require a sub with this setup. These speakers provide the exact amount of bass that I was hoping for.

Did you run TRS to TRS, or TRS to the Unbalanced RCA jack on the speakers?

That the relationship can vary dramatically with the enclosure design and woofer design, sure.

Yamaha N3X, which I think does a fine job of simulating a 6ft piano in terms of loudness and frequency coverage, has (16 cm + 13 cm + 2.5 cm) x 4 speaker array.

The N2, speakers of which is more satisfying to me as a player than the N3X, has these speaker specs: (13cm + 2.5cm) x 3 + (8cm + 2.5cm) + 16cm x 2.

The N1UX, which is pretty good, but not as good as the N2 has these specs: (16 cm + 1.9 cm) x 2

The largest speakers for all of them is 16cm or 6.3 inches.

I personally believe what would make a digital piano sound good is the loudness capability, a wide image (more than 2 speakers), low frequency extension (but not subwoofer low), and the correct EQ adjustment for the player position and/or the wall.

After reading all your answers my conclusion is that there's nothing wrong with my speakers, but being 3" they just happen to be to small for the task. Maybe I'll buy something bigger and use the small ones for other purposes.

Exactly so. And so the notion of this "relationship" is a red herring. There is no relationship.

Re Sweelinck and 3xMac: Add room acoustics (e.g. resonance frequencies) to the variables. Extremely important for bass reproduction as most will know.

The only way to get a "natural" sound from your speakers, in any given room, is to experiment (with reason and background knowledge, to be sure).

And, by the way: The length of the acoustic piano your systems aims to reproduce is certainly not a very important variable here, as others have pointed out. You wouldn't put a concert grand in a tiny room either...

I use a pair of JBL LSR 305 5" monitors along a LSR 310S 10" subwoofer and, with a tiny LSR 310S volume, the bass notes are magnificent.

Beware of those sounds travelling through the building structure, if you go a similar way... Don't ask me why I know

Why do you know?

I went TRS to TRS.

Two issues: feel and frequency....

Frequency... to go low, a speaker needs to move more air and in a bigger way as low frequency sound waves are literally large. To do this, speakers, or woofers for those focused on lower frequencies usually get larger. But to make a speaker small, designers can employ tricks such as designing ports and such. There is no fast rule, but bigger is generally lower and better.

Feel: You need to move alot of air to feel those low notes.... for this, you generally need a large speaker. Big pianos have large sound generating areas and that an affect on both the quality of sound and the feel you get. Hard to match that feel as it is more than just frequency, but the whole sound generation system.

Another general rule of thumb: more money gets you more/better sound quality overall, and more accurate bass.

Peace
Bruce in Philly

Yes. Having more than one room dimension be identical is especially problematic, with a cube-shaped room being the worst case. Bass traps can be used to defeat standing waves. But this is primarily a problem if you have a subwoofer in a smaller room.